An explosive device went off outside a cinema in a busy part of the capital, injuring one person late on Saturday, a police officer said.
The person wounded in the explosion in Nairobi was a handcart pusher and had been given a small piece of luggage by an unknown person who fled, the official said.
Detectives believe inside the luggage was an improvised explosive device that went off, he said.
The officer spoke on the condition of anonymity because he was not authorised to speak to reporters.
The Kenya Red Cross said it sent emergency teams to the scene, which was sealed off by law enforcement officers.
The explosion happened two days after the US Embassy in Nairobi issued a security alert reminding the public about “the continued need for sustained vigilance in public spaces such as shopping malls, hotels, and places of worship”.
Kenya is recovering from a January 15 attack in which gunmen stormed a hotel complex and killed 21 people.
The extremist group Al-Shabaab, which is based in neighbouring Somalia, claimed responsibility for the attack on the DusitD2 hotel and shopping complex.
Al-Shabaab, which has ties with Al-Qaeda, has often targeted Kenya in retaliation over Kenya’s military involvement in Somalia.